Robertson and Seymour conjectured that the treewidth of a planar graph and the treewidth of its geometric dual di er by at most one. Lapoire solved the conjecture in the a rmative, using algebraic techniques. We give here a much shorter proof of this result.
Weak embedding of planar graphs
β Scribed by Wei Erling; Liu Yanpei
- Publisher
- Springer-Verlag
- Year
- 2006
- Tongue
- English
- Weight
- 217 KB
- Volume
- 21
- Category
- Article
- ISSN
- 1598-5865
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We present a dynamic data structure for the incremental construction of a planar embedding of a planar graph. The data structure supports the following Ε½ . operations: i testing if a new edge can be added to the embedding without Ε½ . introducing crossing; and ii adding vertices and edges. The time c
It will be shown that the number of equivalence classes of embeddings of a 3-connected nonplanar graph into a projective plane coincides with the number of isomorphism classes of planar double coverings of the graph and a combinatorial method to determine the number will be developed.